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14 Mar 2025, 06:06
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
58% (02:57) correct
42%
(02:56)
wrong
based on 89
sessions
History
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Not Attempted Yet
The figure given shows a seating plan for 7 people Amy, Bob, Charlie, David, Ella, Fiona, and Garry in a room. Spot numbered 1 is to be taken by Amy, or Bob, or Charlie. David and Garry do not want to sit adjacent to each other in the same row. How many different seating arrangements are possible?
(A) 144
(B) 432
(C) 576
(D) 1584
(E) 2160
(A) 144
(B) 432
(C) 576
(D) 1584
(E) 2160
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Screenshot-jambore.png [ 41.77 KiB | Viewed 1663 times ]
14 Mar 2025, 06:32
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Let's break it down into two cases,
Case 1: David or Garry sit in the top row (Both can't sit since seat 1 is already occupied by A, B, or C)
Row 1: 2 * 3 * 2 * 4 (Multiplying by 2 is essentially 3*2*4 or 3*4*2 since D or G can sit on seat 2 or 3)
Row 2: 4 * 3 * 2 * 1
Case 1 gives 2*24*24
Case 2: David and Garry sit in the second row
Row 1: 3 * 4 * 3
Row 2: 4! - 3!*2! (Total arrangements - arrangements where D and G are together)
Case 2 gives 36*12
Adding both cases to get the answer
2*24*24 + 36*12 = 12*12*(8+3) = 144*11 = 1584
Answer D.
Case 1: David or Garry sit in the top row (Both can't sit since seat 1 is already occupied by A, B, or C)
Row 1: 2 * 3 * 2 * 4 (Multiplying by 2 is essentially 3*2*4 or 3*4*2 since D or G can sit on seat 2 or 3)
Row 2: 4 * 3 * 2 * 1
Case 1 gives 2*24*24
Case 2: David and Garry sit in the second row
Row 1: 3 * 4 * 3
Row 2: 4! - 3!*2! (Total arrangements - arrangements where D and G are together)
Case 2 gives 36*12
Adding both cases to get the answer
2*24*24 + 36*12 = 12*12*(8+3) = 144*11 = 1584
Answer D.
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